In the work of [1]} ([1]}, [3]}), they solved this problem by a model selection procedure via some suitable penalty function based on the partitions given by the pruned dynamic programming algorithm (PDPA for short) proposed by [4]}. Given \(N_{\max }\)  the maximum number of segments for consideration, for each integer \(\lambda \)  with \(1\le \lambda \le N_{\max }\) , PDPA searches the optimal partition with exact \(\lambda \)  segments. We set \(N_{\max }=30\)  hence 30 different partitions of the sequence \(1,\ldots ,n\)  are returned by PDPA. Provided a partition, the value of \({\gamma }^{*}\)  on each segment is given by maximum likelihood estimation as it was done in [1]} ([1]}, [3]}). By doing so, we collect 30 candidates which we denote as \(\widehat{\Gamma }_{c}=\lbrace \widehat{{\gamma }}_{\lambda }, 1\le \lambda \le N_{\max }\rbrace \) .
